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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>st_ility</b> -  stabilizability test</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[ns, [nc, [,U [,Slo] ]]]=st_ility(Sl [,tol])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>Sl</b>
        </tt>: <tt>
          <b>syslin</b>
        </tt> list (linear system)</li>
      <li>
        <tt>
          <b>ns</b>
        </tt>:  integer (dimension of stabilizable subspace)</li>
      <li>
        <tt>
          <b>nc</b>
        </tt>:  integer (dimension of controllable subspace <tt>
          <b>nc &lt;= ns</b>
        </tt>)</li>
      <li>
        <tt>
          <b>U</b>
        </tt>: basis such that its <tt>
          <b>ns</b>
        </tt> (resp. <tt>
          <b>nc</b>
        </tt>) first components span the stabilizable (resp. controllable) subspace</li>
      <li>
        <tt>
          <b>Slo</b>
        </tt>: a linear system (<tt>
          <b>syslin</b>
        </tt> list)</li>
      <li>
        <tt>
          <b>tol</b>
        </tt>: threshold for controllability detection (see contr)</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b> Slo=( U'*A*U, U'*B, C*U, D, U'*x0 )</b>
      </tt> (<tt>
        <b>syslin</b>
      </tt> list)
    displays the stabilizable form of <tt>
        <b>Sl</b>
      </tt>. Stabilizability means
    <tt>
        <b>ns=nx</b>
      </tt> (dim. of <tt>
        <b>A</b>
      </tt> matrix).</p>
    <pre>

         [*,*,*]            [*]
U'*A*U = [0,*,*]     U'*B = [0]
         [0,0,*]            [0]
   
    </pre>
    <p>
    where <tt>
        <b> (A11,B1) </b>
      </tt> (dim(A11)= <tt>
        <b>nc</b>
      </tt>) is controllable and <tt>
        <b>A22</b>
      </tt> 
    (dim(A22)=<tt>
        <b>ns-nc</b>
      </tt>) is stable.
    "Stable" means real part of eigenvalues negative for a continuous
    linear system, and magnitude of eigenvalues lower than one for a
    discrete-time system (as defined by <tt>
        <b>syslin</b>
      </tt>).</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

A=diag([0.9,-2,3]);B=[0;0;1];Sl=syslin('c',A,B,[]);
[ns,nc,U]=st_ility(Sl);
U'*A*U
U'*B
[ns,nc,U]=st_ility(syslin('d',A,B,[]));
U'*A*U
U'*B
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="dt_ility.htm">
        <tt>
          <b>dt_ility</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="contr.htm">
        <tt>
          <b>contr</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="stabil.htm">
        <tt>
          <b>stabil</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../elementary/ssrand.htm">
        <tt>
          <b>ssrand</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>S. Steer INRIA 1988</p>
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